@inbook{193577dc62c545dca1493040ee6ba7eb,
title = "Asymptotic Behavior of Solutions for a Fourth Order Parabolic Equation with Gradient Nonlinearity via the Galerkin Method",
abstract = "In this paper we consider the initial-boundary value problem for a fourth order parabolic equation with gradient nonlinearity. The problem is regarded as the L2-gradient flow for an energy functional which is unbounded from below. We first prove the existence and the uniqueness of solutions to the problem via the Galerkin method. Moreover, combining the potential well method with the Galerkin method, we study the asymptotic behavior of global-in-time solutions to the problem.",
keywords = "Epitaxial growth, Fourth order parabolic equation, Galerkin method, Gradient nonlinearity",
author = "Nobuhito Miyake and Shinya Okabe",
note = "Funding Information: Acknowledgments The authors would like to thank the referees for their careful readings and useful comments. The first author was supported in part by the Grant-in-Aid for JSPS Fellows (No. JP19J10424) from Japan Society for the Promotion of Science. The second author was supported in part by the Grant-in-Aid for Scientific Research(S) (No. JP19H05599) from Japan Society for the Promotion of Science. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2021",
doi = "10.1007/978-3-030-73363-6_12",
language = "English",
series = "Springer INdAM Series",
publisher = "Springer-Verlag Italia s.r.l.",
pages = "247--271",
booktitle = "Springer INdAM Series",
}